FFTPoissonSolver.cpp 25.2 KB
 gsell committed Mar 15, 2012 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 // -*- C++ -*- /*************************************************************************** * * * FFTPoissonSolver.cc * * * * * * * ***************************************************************************/ // include files  kraus committed Oct 20, 2014 16 #include "Solvers/FFTPoissonSolver.h"  gsell committed Mar 15, 2012 17 18 19 20 21 22 23 24 25 26 #include "Algorithms/PartBunch.h" #include "Physics/Physics.h" #include ////////////////////////////////////////////////////////////////////////////// // a little helper class to specialize the action of the Green's function // calculation. This should be specialized for each dimension // to the proper action for computing the Green's function. The first // template parameter is the full type of the Field to compute, and the second // is the dimension of the data, which should be specialized.  27 28 29 30 #ifdef OPAL_NOCPLUSPLUS11_NULLPTR #define nullptr NULL #endif  gsell committed Mar 15, 2012 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 template struct SpecializedGreensFunction { }; template<> struct SpecializedGreensFunction<3> { template static void calculate(Vektor &hrsq, FT &grn, FT2 *grnI) { grn = grnI[0] * hrsq[0] + grnI[1] * hrsq[1] + grnI[2] * hrsq[2]; grn = 1.0 / sqrt(grn); grn[0][0][0] = grn[0][0][1]; } }; //////////////////////////////////////////////////////////////////////////// // constructor  adelmann committed Feb 13, 2013 49 FFTPoissonSolver::FFTPoissonSolver(Mesh_t *mesh, FieldLayout_t *fl, std::string greensFunction, std::string bcz):  gsell committed Mar 15, 2012 50 51  mesh_m(mesh), layout_m(fl),  Yves Ineichen committed Mar 31, 2012 52 53 54 55  mesh2_m(nullptr), layout2_m(nullptr), mesh3_m(nullptr), layout3_m(nullptr),  56 57  mesh4_m(nullptr), layout4_m(nullptr),  gsell committed Mar 15, 2012 58 59  greensFunction_m(greensFunction) { int i;  kraus committed Oct 20, 2014 60   adelmann committed Jun 18, 2013 61  bcz_m = (bcz==std::string("PERIODIC")); // for DC beams, the z direction has periodic boundary conditions  kraus committed Oct 20, 2014 62   gsell committed Mar 15, 2012 63 64 65 66 67 68 69 70 71 72 73  domain_m = layout_m->getDomain(); // For efficiency in the FFT's, we can use a parallel decomposition // which can be serial in the first dimension. e_dim_tag decomp[3]; e_dim_tag decomp2[3]; for(int d = 0; d < 3; ++d) { decomp[d] = layout_m->getRequestedDistribution(d); decomp2[d] = layout_m->getRequestedDistribution(d); }  adelmann committed Jun 18, 2013 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92  if (bcz_m) { // The FFT's require double-sized field sizes in order to // simulate an isolated system. The FFT of the charge density field, rho, // would otherwise mimic periodic boundary conditions, i.e. as if there were // several beams set a periodic distance apart. The double-sized fields in x and // alleviate this problem, in z we have periodic BC's for(i = 0; i < 2; i++) { hr_m[i] = mesh_m->get_meshSpacing(i); nr_m[i] = domain_m[i].length(); domain2_m[i] = Index(2 * nr_m[i] + 1); } hr_m[2] = mesh_m->get_meshSpacing(2); nr_m[2] = domain_m[2].length(); domain2_m[2] = Index(2 * nr_m[2] + 1); for(i = 0; i < 2 * 3; ++i) { bc_m[i] = new ZeroFace(i); vbc_m[i] = new ZeroFace(i);  kraus committed Oct 20, 2014 93  }  adelmann committed Jun 18, 2013 94 95 96 97 98  // z-direction bc_m[4] = new ParallelPeriodicFace(4); bc_m[5] = new ParallelPeriodicFace(5); vbc_m[4] = new ZeroFace(4); vbc_m[5] = new ZeroFace(5);  kraus committed Oct 20, 2014 99  }  adelmann committed Jun 18, 2013 100 101 102 103 104 105 106  else { // The FFT's require double-sized field sizes in order to // simulate an isolated system. The FFT of the charge density field, rho, // would otherwise mimic periodic boundary conditions, i.e. as if there were // several beams set a periodic distance apart. The double-sized fields // alleviate this problem. for(i = 0; i < 3; i++) {  gsell committed Mar 15, 2012 107 108 109  hr_m[i] = mesh_m->get_meshSpacing(i); nr_m[i] = domain_m[i].length(); domain2_m[i] = Index(2 * nr_m[i] + 1);  adelmann committed Jun 18, 2013 110 111 112 113 114  } for(i = 0; i < 2 * 3; ++i) { bc_m[i] = new ZeroFace(i); vbc_m[i] = new ZeroFace(i);  kraus committed Oct 20, 2014 115  }  gsell committed Mar 15, 2012 116 117 118  } // create double sized mesh and layout objects for the use in the FFT's  Yves Ineichen committed Mar 31, 2012 119 120  mesh2_m = std::unique_ptr(new Mesh_t(domain2_m)); layout2_m = std::unique_ptr(new FieldLayout_t(*mesh2_m, decomp));  gsell committed Mar 15, 2012 121 122  rho2_m.initialize(*mesh2_m, *layout2_m);  adelmann committed Jun 18, 2013 123   gsell committed Mar 15, 2012 124 125 126 127 128 129 130 131 132 133 134 135  NDIndex<3> tmpdomain; // Create the domain for the transformed (complex) fields. Do this by // taking the domain from the doubled mesh, permuting it to the right, and // setting the 2nd dimension to have n/2 + 1 elements. domain3_m[0] = Index(2 * nr_m[3-1] + 1); domain3_m[1] = Index(nr_m[0] + 2); for(i = 2; i < 3; ++i) domain3_m[i] = Index(2 * nr_m[i-1] + 1); // create mesh and layout for the new real-to-complex FFT's, for the // complex transformed fields  Yves Ineichen committed Mar 31, 2012 136 137  mesh3_m = std::unique_ptr(new Mesh_t(domain3_m)); layout3_m = std::unique_ptr(new FieldLayout_t(*mesh3_m, decomp2));  kraus committed Oct 20, 2014 138   gsell committed Mar 15, 2012 139 140 141 142 143 144 145  rho2tr_m.initialize(*mesh3_m, *layout3_m); imgrho2tr_m.initialize(*mesh3_m, *layout3_m); grntr_m.initialize(*mesh3_m, *layout3_m); // helper field for sin greentr_m.initialize(*mesh3_m, *layout3_m);  146 147 148 149 150 151 152 153  for(i = 0; i < 3; i++) { domain4_m[i] = Index(nr_m[i] + 2); } mesh4_m = std::unique_ptr(new Mesh_t(domain4_m)); layout4_m = std::unique_ptr(new FieldLayout_t(*mesh4_m, decomp)); tmpgreen.initialize(*mesh4_m, *layout4_m);  gsell committed Mar 15, 2012 154 155 156 157 158 159 160 161  // create a domain used to indicate to the FFT's how to construct it's // temporary fields. This is the same as the complex field's domain, // but permuted back to the left. tmpdomain = layout3_m->getDomain(); for(i = 0; i < 3; ++i) domainFFTConstruct_m[i] = tmpdomain[(i+1) % 3]; // create the FFT object  Yves Ineichen committed Mar 31, 2012 162  fft_m = std::unique_ptr(new FFT_t(layout2_m->getDomain(), domainFFTConstruct_m));  gsell committed Mar 15, 2012 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178  // these are fields that are used for calculating the Green's function. // they eliminate some calculation at each time-step. for(i = 0; i < 3; ++i) { grnIField_m[i].initialize(*mesh2_m, *layout2_m); grnIField_m[i][domain2_m] = where(lt(domain2_m[i], nr_m[i]), domain2_m[i] * domain2_m[i], (2 * nr_m[i] - domain2_m[i]) * (2 * nr_m[i] - domain2_m[i])); } GreensFunctionTimer_m = IpplTimings::getTimer("GreensFTotal"); IntGreensFunctionTimer1_m = IpplTimings::getTimer("IntGreenF1"); IntGreensFunctionTimer2_m = IpplTimings::getTimer("IntGreenF2"); IntGreensFunctionTimer3_m = IpplTimings::getTimer("IntGreenF3");  179  IntGreensMirrorTimer1_m = IpplTimings::getTimer("MirrorRho1");  gsell committed Mar 15, 2012 180 181 182 183 184  ShIntGreensFunctionTimer1_m = IpplTimings::getTimer("ShIntGreenF1"); ShIntGreensFunctionTimer2_m = IpplTimings::getTimer("ShIntGreenF2"); ShIntGreensFunctionTimer3_m = IpplTimings::getTimer("ShIntGreenF3"); ShIntGreensFunctionTimer4_m = IpplTimings::getTimer("ShIntGreenF4");  185  IntGreensMirrorTimer2_m = IpplTimings::getTimer("MirrorRho2");  gsell committed Mar 15, 2012 186 187 188 189 190 191 192 193 194 195 196  GreensFunctionTimer1_m = IpplTimings::getTimer("GreenF1"); GreensFunctionTimer2_m = IpplTimings::getTimer("GreenF2"); GreensFunctionTimer3_m = IpplTimings::getTimer("GreenF3"); GreensFunctionTimer4_m = IpplTimings::getTimer("GreenF4"); } FFTPoissonSolver::FFTPoissonSolver(PartBunch &beam, std::string greensFunction): mesh_m(&beam.getMesh()), layout_m(&beam.getFieldLayout()),  Yves Ineichen committed Mar 31, 2012 197 198 199 200  mesh2_m(nullptr), layout2_m(nullptr), mesh3_m(nullptr), layout3_m(nullptr),  201 202  mesh4_m(nullptr), layout4_m(nullptr),  gsell committed Mar 15, 2012 203 204 205 206  greensFunction_m(greensFunction) { int i; domain_m = layout_m->getDomain();  adelmann committed Jun 18, 2013 207 208 209 210  INFOMSG("FFTPoissonSolver(PartBunch &beam ..." << endl;);  gsell committed Mar 15, 2012 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231  // For efficiency in the FFT's, we can use a parallel decomposition // which can be serial in the first dimension. e_dim_tag decomp[3]; e_dim_tag decomp2[3]; for(int d = 0; d < 3; ++d) { decomp[d] = layout_m->getRequestedDistribution(d); decomp2[d] = layout_m->getRequestedDistribution(d); } // The FFT's require double-sized field sizes in order to (more closely // do not understand this ...) // simulate an isolated system. The FFT of the charge density field, rho, // would otherwise mimic periodic boundary conditions, i.e. as if there were // several beams set a periodic distance apart. The double-sized fields // alleviate this problem. for(i = 0; i < 3; i++) { hr_m[i] = mesh_m->get_meshSpacing(i); nr_m[i] = domain_m[i].length(); domain2_m[i] = Index(2 * nr_m[i] + 1); } // create double sized mesh and layout objects for the use in the FFT's  Yves Ineichen committed Mar 31, 2012 232 233  mesh2_m = std::unique_ptr(new Mesh_t(domain2_m)); layout2_m = std::unique_ptr(new FieldLayout_t(*mesh2_m, decomp));  gsell committed Mar 15, 2012 234 235 236 237 238 239 240 241 242 243 244 245 246 247  rho2_m.initialize(*mesh2_m, *layout2_m); NDIndex<3> tmpdomain; // Create the domain for the transformed (complex) fields. Do this by // taking the domain from the doubled mesh, permuting it to the right, and // setting the 2nd dimension to have n/2 + 1 elements. domain3_m[0] = Index(2 * nr_m[3-1] + 1); domain3_m[1] = Index(nr_m[0] + 2); for(i = 2; i < 3; ++i) domain3_m[i] = Index(2 * nr_m[i-1] + 1); // create mesh and layout for the new real-to-complex FFT's, for the // complex transformed fields  Yves Ineichen committed Mar 31, 2012 248 249  mesh3_m = std::unique_ptr(new Mesh_t(domain3_m)); layout3_m = std::unique_ptr(new FieldLayout_t(*mesh3_m, decomp2));  gsell committed Mar 15, 2012 250 251 252 253 254 255 256  rho2tr_m.initialize(*mesh3_m, *layout3_m); imgrho2tr_m.initialize(*mesh3_m, *layout3_m); grntr_m.initialize(*mesh3_m, *layout3_m); // helper field for sin greentr_m.initialize(*mesh3_m, *layout3_m);  257 258 259 260 261 262 263 264  for(i = 0; i < 3; i++) { domain4_m[i] = Index(nr_m[i] + 2); } mesh4_m = std::unique_ptr(new Mesh_t(domain4_m)); layout4_m = std::unique_ptr(new FieldLayout_t(*mesh4_m, decomp)); tmpgreen.initialize(*mesh4_m, *layout4_m);  gsell committed Mar 15, 2012 265 266 267 268 269 270 271 272  // create a domain used to indicate to the FFT's how to construct it's // temporary fields. This is the same as the complex field's domain, // but permuted back to the left. tmpdomain = layout3_m->getDomain(); for(i = 0; i < 3; ++i) domainFFTConstruct_m[i] = tmpdomain[(i+1) % 3]; // create the FFT object  Yves Ineichen committed Mar 31, 2012 273  fft_m = std::unique_ptr(new FFT_t(layout2_m->getDomain(), domainFFTConstruct_m));  gsell committed Mar 15, 2012 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289  // these are fields that are used for calculating the Green's function. // they eliminate some calculation at each time-step. for(i = 0; i < 3; ++i) { grnIField_m[i].initialize(*mesh2_m, *layout2_m); grnIField_m[i][domain2_m] = where(lt(domain2_m[i], nr_m[i]), domain2_m[i] * domain2_m[i], (2 * nr_m[i] - domain2_m[i]) * (2 * nr_m[i] - domain2_m[i])); } } //////////////////////////////////////////////////////////////////////////// // destructor FFTPoissonSolver::~FFTPoissonSolver() { // delete the FFT object  Yves Ineichen committed Mar 31, 2012 290  //~ delete fft_m;  gsell committed Mar 15, 2012 291 292  // delete the mesh and layout objects  Yves Ineichen committed Mar 31, 2012 293 294 295 296  //~ if(mesh2_m != 0) delete mesh2_m; //~ if(layout2_m != 0) delete layout2_m; //~ if(mesh3_m != 0) delete mesh3_m; //~ if(layout3_m != 0) delete layout3_m;  gsell committed Mar 15, 2012 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 } //////////////////////////////////////////////////////////////////////////// // given a charge-density field rho and a set of mesh spacings hr, // compute the electric potential from the image charge by solving // the Poisson's equation void FFTPoissonSolver::computePotential(Field_t &rho, Vector_t hr, double zshift) { // use grid of complex doubled in both dimensions // and store rho in lower left quadrant of doubled grid rho2_m = 0.0; rho2_m[domain_m] = rho[domain_m]; // needed in greens function hr_m = hr; // FFT double-sized charge density // we do a backward transformation so that we dont have to account for the normalization factor // that is used in the forward transformation of the IPPL FFT fft_m->transform(-1, rho2_m, rho2tr_m); // must be called if the mesh size has changed // have to check if we can do G with h = (1,1,1) // and rescale later // Do image charge. // The minus sign is due to image charge. // Convolute transformed charge density with shifted green's function. IpplTimings::startTimer(GreensFunctionTimer_m); shiftedIntGreensFunction(zshift); IpplTimings::stopTimer(GreensFunctionTimer_m); // Multiply transformed charge density and // transformed Green's function. Don't divide // by (2*nx_m)*(2*ny_m), as Ryne does; this // normalization is done in POOMA's fft routine. imgrho2tr_m = - rho2tr_m * grntr_m; // Inverse FFT to find image charge potential, rho2_m equals the electrostatic potential. fft_m->transform(+1, imgrho2tr_m, rho2_m); // Re-use rho to store image potential. Flip z coordinate since this is a mirror image. Index I = nr_m[0]; Index J = nr_m[1]; Index K = nr_m[2]; rho[I][J][K] = rho2_m[I][J][nr_m[2] - K - 1]; } //////////////////////////////////////////////////////////////////////////// // given a charge-density field rho and a set of mesh spacings hr, // compute the electric field and put in eg by solving the Poisson's equation void FFTPoissonSolver::computePotential(Field_t &rho, Vector_t hr) { // use grid of complex doubled in both dimensions // and store rho in lower left quadrant of doubled grid rho2_m = 0.0; rho2_m[domain_m] = rho[domain_m]; // needed in greens function hr_m = hr; // FFT double-sized charge density // we do a backward transformation so that we dont have to account for the normalization factor // that is used in the forward transformation of the IPPL FFT fft_m->transform(-1, rho2_m, rho2tr_m); // must be called if the mesh size has changed // have to check if we can do G with h = (1,1,1) // and rescale later IpplTimings::startTimer(GreensFunctionTimer_m); if(greensFunction_m == std::string("INTEGRATED")) integratedGreensFunction(); else greensFunction(); IpplTimings::stopTimer(GreensFunctionTimer_m); // multiply transformed charge density // and transformed Green function // Don't divide by (2*nx_m)*(2*ny_m), as Ryne does; // this normalization is done in POOMA's fft routine. rho2tr_m *= grntr_m; // inverse FFT, rho2_m equals to the electrostatic potential fft_m->transform(+1, rho2tr_m, rho2_m); // end convolution // back to physical grid // reuse the charge density field to store the electrostatic potential rho[domain_m] = rho2_m[domain_m]; } /////////////////////////////////////////////////////////////////////////// // calculate the FFT of the Green's function for the given field void FFTPoissonSolver::greensFunction() { //hr_m[0]=hr_m[1]=hr_m[2]=1; Vector_t hrsq(hr_m * hr_m); IpplTimings::startTimer(GreensFunctionTimer1_m); SpecializedGreensFunction<3>::calculate(hrsq, rho2_m, grnIField_m); IpplTimings::stopTimer(GreensFunctionTimer1_m); // Green's function calculation complete at this point. // The next step is to FFT it. // FFT of Green's function // ofstream fstr; // fstr.precision(9); // fstr.open("green",ios::out); // for (int i=0;itransform(-1, rho2_m, grntr_m); IpplTimings::stopTimer(GreensFunctionTimer4_m); // ofstream fstr2; // fstr2.precision(9); // fstr2.open("green_fft",ios::out); // for (int i=0;i> transverse size the * direct Green function at each mesh point is not efficient * (needs a lot of mesh points along the transverse size to * get a good resolution) * * If the charge density function is uniform within each cell * the following Green's function can be defined: * * \f[ \overline{G}(x_i - x_{i'}, y_j - y_{j'}, z_k - z_{k'} cout << I << endl; cout << J << endl; cout << K << endl; cout << IE << endl; cout << JE << endl; cout << KE << endl; ) = \int_{x_{i'} - h_x/2}^{x_{i'} + h_x/2} dx' \int_{y_{j'} - h_y/2}^{y_{j'} + h_y/2} dy' \int_{z_{k'} - h_z/2}^{z_{k'} + h_z/2} dz' G(x_i - x_{i'}, y_j - y_{j'}, z_k - z_{k'}). * \f] */ void FFTPoissonSolver::integratedGreensFunction() {  444 445  NDIndex<3> idx = layout4_m->getLocalNDIndex(); double cellVolume = hr_m[0] * hr_m[1] * hr_m[2];  gsell committed Mar 15, 2012 446 447 448 449 450 451 452  tmpgreen = 0.0; IpplTimings::startTimer(IntGreensFunctionTimer1_m); /** * This integral can be calculated analytically in a closed from: */  453 454 455  for(int k = idx[2].first(); k <= idx[2].last() + 1; k++) { for(int j = idx[1].first(); j <= idx[1].last() + 1; j++) { for(int i = idx[0].first(); i <= idx[0].last() + 1; i++) {  gsell committed Mar 15, 2012 456 457 458 459 460 461  Vector_t vv = Vector_t(0.0); vv(0) = i * hr_m[0] - hr_m[0] / 2; vv(1) = j * hr_m[1] - hr_m[1] / 2; vv(2) = k * hr_m[2] - hr_m[2] / 2;  462 463  double r = sqrt(vv(0) * vv(0) + vv(1) * vv(1) + vv(2) * vv(2)); double tmpgrn = -vv(2) * vv(2) * atan(vv(0) * vv(1) / (vv(2) * r)) / 2;  gsell committed Mar 15, 2012 464 465 466 467 468 469  tmpgrn += -vv(1) * vv(1) * atan(vv(0) * vv(2) / (vv(1) * r)) / 2; tmpgrn += -vv(0) * vv(0) * atan(vv(1) * vv(2) / (vv(0) * r)) / 2; tmpgrn += vv(1) * vv(2) * log(vv(0) + r); tmpgrn += vv(0) * vv(2) * log(vv(1) + r); tmpgrn += vv(0) * vv(1) * log(vv(2) + r);  470  tmpgreen[i][j][k] = tmpgrn / cellVolume;  gsell committed Mar 15, 2012 471 472 473 474 475 476 477 478  } } } IpplTimings::stopTimer(IntGreensFunctionTimer1_m); IpplTimings::startTimer(IntGreensFunctionTimer2_m);  479 480 481 482 483 484  //assign seems to have problems when we need values that are on another CPU, i.e. [I+1] /*assign(rho2_m[I][J][K] , tmpgreen[I+1][J+1][K+1] - tmpgreen[I][J+1][K+1] - tmpgreen[I+1][J][K+1] + tmpgreen[I][J][K+1] - tmpgreen[I+1][J+1][K] + tmpgreen[I][J+1][K] + tmpgreen[I+1][J][K] - tmpgreen[I][J][K]);*/  gsell committed Mar 15, 2012 485 486 487 488 489 490  Index I = nr_m[0] + 1; Index J = nr_m[1] + 1; Index K = nr_m[2] + 1; // the actual integration  491  rho2_m = 0.0;  gsell committed Mar 15, 2012 492 493 494 495 496 497 498 499 500 501 502  rho2_m[I][J][K] = tmpgreen[I+1][J+1][K+1]; rho2_m[I][J][K] += tmpgreen[I+1][J][K]; rho2_m[I][J][K] += tmpgreen[I][J+1][K]; rho2_m[I][J][K] += tmpgreen[I][J][K+1]; rho2_m[I][J][K] -= tmpgreen[I+1][J+1][K]; rho2_m[I][J][K] -= tmpgreen[I+1][J][K+1]; rho2_m[I][J][K] -= tmpgreen[I][J+1][K+1]; rho2_m[I][J][K] -= tmpgreen[I][J][K]; IpplTimings::stopTimer(IntGreensFunctionTimer2_m);  kraus committed Apr 16, 2012 503  mirrorRhoField();  gsell committed Mar 15, 2012 504   505  IpplTimings::startTimer(IntGreensFunctionTimer3_m);  gsell committed Mar 15, 2012 506  fft_m->transform(-1, rho2_m, grntr_m);  507  IpplTimings::stopTimer(IntGreensFunctionTimer3_m);  gsell committed Mar 15, 2012 508 509 510 511 512 } void FFTPoissonSolver::shiftedIntGreensFunction(double zshift) { tmpgreen = 0.0;  513  Field_t grn2(*mesh4_m, *layout4_m);  gsell committed Mar 15, 2012 514  grn2 = 0.0;  515 516  NDIndex<3> idx = layout4_m->getLocalNDIndex(); double cellVolume = hr_m[0] * hr_m[1] * hr_m[2];  gsell committed Mar 15, 2012 517  IpplTimings::startTimer(ShIntGreensFunctionTimer1_m);  518 519 520  for(int k = idx[2].first(); k <= idx[2].last(); k++) { for(int j = idx[1].first(); j <= idx[1].last(); j++) { for(int i = idx[0].first(); i <= idx[0].last(); i++) {  gsell committed Mar 15, 2012 521 522 523 524 525 526  Vector_t vv = Vector_t(0.0); vv(0) = i * hr_m[0] - hr_m[0] / 2; vv(1) = j * hr_m[1] - hr_m[1] / 2; vv(2) = k * hr_m[2] - hr_m[2] / 2 + zshift;  527 528  double r = sqrt(vv(0) * vv(0) + vv(1) * vv(1) + vv(2) * vv(2)); double tmpgrn = -vv(2) * vv(2) * atan(vv(0) * vv(1) / (vv(2) * r)) / 2;  gsell committed Mar 15, 2012 529 530 531 532 533 534  tmpgrn += -vv(1) * vv(1) * atan(vv(0) * vv(2) / (vv(1) * r)) / 2; tmpgrn += -vv(0) * vv(0) * atan(vv(1) * vv(2) / (vv(0) * r)) / 2; tmpgrn += vv(1) * vv(2) * log(vv(0) + r); tmpgrn += vv(0) * vv(2) * log(vv(1) + r); tmpgrn += vv(0) * vv(1) * log(vv(2) + r);  535  tmpgreen[i][j][k] = tmpgrn / cellVolume;  gsell committed Mar 15, 2012 536 537 538 539 540 541 542  } } } IpplTimings::stopTimer(ShIntGreensFunctionTimer1_m); IpplTimings::startTimer(ShIntGreensFunctionTimer2_m);  543 544 545  for(int k = idx[2].first(); k <= idx[2].last(); k++) { for(int j = idx[1].first(); j <= idx[1].last(); j++) { for(int i = idx[0].first(); i <= idx[0].last(); i++) {  gsell committed Mar 15, 2012 546 547 548 549  Vector_t vv = Vector_t(0.0); vv(0) = i * hr_m[0] - hr_m[0] / 2; vv(1) = j * hr_m[1] - hr_m[1] / 2;  550  vv(2) = k * hr_m[2] - hr_m[2] / 2 + zshift - nr_m[2] * hr_m[2];  gsell committed Mar 15, 2012 551   552 553  double r = sqrt(vv(0) * vv(0) + vv(1) * vv(1) + vv(2) * vv(2)); double tmpgrn = -vv(2) * vv(2) * atan(vv(0) * vv(1) / (vv(2) * r)) / 2;  gsell committed Mar 15, 2012 554 555 556 557 558 559  tmpgrn += -vv(1) * vv(1) * atan(vv(0) * vv(2) / (vv(1) * r)) / 2; tmpgrn += -vv(0) * vv(0) * atan(vv(1) * vv(2) / (vv(0) * r)) / 2; tmpgrn += vv(1) * vv(2) * log(vv(0) + r); tmpgrn += vv(0) * vv(2) * log(vv(1) + r); tmpgrn += vv(0) * vv(1) * log(vv(2) + r);  560  grn2[i][j][k] = tmpgrn / cellVolume;  gsell committed Mar 15, 2012 561 562 563 564 565 566  } } } IpplTimings::stopTimer(ShIntGreensFunctionTimer2_m);  567 568 569 570 571 572 573 574 575 576 577  /** ** (x[0:nr_m[0]-1]^2 + y[0:nr_m[1]-1]^2 + (z_c + z[0:nr_m[2]-1])^2)^{-0.5} ** (x[nr_m[0]:1]^2 + y[0:nr_m[1]-1]^2 + (z_c + z[0:nr_m[2]-1])^2)^{-0.5} ** (x[0:nr_m[0]-1]^2 + y[nr_m[1]:1]^2 + (z_c + z[0:nr_m[2]-1])^2)^{-0.5} ** (x[nr_m[0]:1]^2 + y[nr_m[1]:1]^2 + (z_c + z[0:nr_m[2]-1])^2)^{-0.5} ** ** (x[0:nr_m[0]-1]^2 + y[0:nr_m[1]-1]^2 + (z_c - z[nr_m[2]:1])^2)^{-0.5} ** (x[nr_m[0]:1]^2 + y[0:nr_m[1]-1]^2 + (z_c - z[nr_m[2]:1])^2)^{-0.5} ** (x[0:nr_m[0]-1]^2 + y[nr_m[1]:1]^2 + (z_c - z[nr_m[2]:1])^2)^{-0.5} ** (x[nr_m[0]:1]^2 + y[nr_m[1]:1]^2 + (z_c - z[nr_m[2]:1])^2)^{-0.5} */  gsell committed Mar 15, 2012 578   579  IpplTimings::startTimer(ShIntGreensFunctionTimer3_m);  gsell committed Mar 15, 2012 580 581 582 583 584 585  Index I = nr_m[0] + 1; Index J = nr_m[1] + 1; Index K = nr_m[2] + 1; // the actual integration  586  rho2_m = 0.0;  gsell committed Mar 15, 2012 587 588 589 590 591 592 593 594  rho2_m[I][J][K] = tmpgreen[I+1][J+1][K+1]; rho2_m[I][J][K] += tmpgreen[I+1][J][K]; rho2_m[I][J][K] += tmpgreen[I][J+1][K]; rho2_m[I][J][K] += tmpgreen[I][J][K+1]; rho2_m[I][J][K] -= tmpgreen[I+1][J+1][K]; rho2_m[I][J][K] -= tmpgreen[I+1][J][K+1]; rho2_m[I][J][K] -= tmpgreen[I][J+1][K+1]; rho2_m[I][J][K] -= tmpgreen[I][J][K];  kraus committed Apr 16, 2012 595   596 597 598 599 600 601 602 603 604  tmpgreen = 0.0; tmpgreen[I][J][K] = grn2[I+1][J+1][K+1]; tmpgreen[I][J][K] += grn2[I+1][J][K]; tmpgreen[I][J][K] += grn2[I][J+1][K]; tmpgreen[I][J][K] += grn2[I][J][K+1]; tmpgreen[I][J][K] -= grn2[I+1][J+1][K]; tmpgreen[I][J][K] -= grn2[I+1][J][K+1]; tmpgreen[I][J][K] -= grn2[I][J+1][K+1]; tmpgreen[I][J][K] -= grn2[I][J][K];  gsell committed Mar 15, 2012 605 606  IpplTimings::stopTimer(ShIntGreensFunctionTimer3_m);  607 608  mirrorRhoField(tmpgreen);  gsell committed Mar 15, 2012 609 610 611 612 613 614  IpplTimings::startTimer(ShIntGreensFunctionTimer4_m); fft_m->transform(-1, rho2_m, grntr_m); IpplTimings::stopTimer(ShIntGreensFunctionTimer4_m); }  kraus committed Apr 16, 2012 615 616 void FFTPoissonSolver::mirrorRhoField() {  617 618 619  IpplTimings::startTimer(IntGreensMirrorTimer1_m); Index aI(0, 2 * nr_m[0]); Index aJ(0, 2 * nr_m[1]);  kraus committed Apr 16, 2012 620   621 622  Index J(0, nr_m[1]); Index K(0, nr_m[2]);  kraus committed Apr 16, 2012 623   624 625 626 627 628 629 630  Index IE(nr_m[0] + 1, 2 * nr_m[0]); Index JE(nr_m[1] + 1, 2 * nr_m[1]); Index KE(nr_m[2] + 1, 2 * nr_m[2]); Index mirroredIE = 2 * nr_m[0] - IE; Index mirroredJE = 2 * nr_m[1] - JE; Index mirroredKE = 2 * nr_m[2] - KE;  kraus committed Apr 16, 2012 631 632 633 634  rho2_m[0][0][0] = rho2_m[0][0][1]; rho2_m[IE][J ][K ] = rho2_m[mirroredIE][J ][K ];  635 636 637 638  rho2_m[aI][JE][K ] = rho2_m[aI ][mirroredJE][K ]; rho2_m[aI][aJ][KE] = rho2_m[aI ][aJ ][mirroredKE]; IpplTimings::stopTimer(IntGreensMirrorTimer1_m);  kraus committed Apr 16, 2012 639 640 641 642 } void FFTPoissonSolver::mirrorRhoField(Field_t & ggrn2) {  643 644 645 646 647 648  IpplTimings::startTimer(IntGreensMirrorTimer2_m); Index aI(0, 2 * nr_m[0]); Index aK(0, 2 * nr_m[2]); Index I(0, nr_m[0]); Index J(0, nr_m[1]);  kraus committed Apr 16, 2012 649   650 651 652  Index IE(nr_m[0] + 1, 2 * nr_m[0]); Index JE(nr_m[1] + 1, 2 * nr_m[1]); Index KE(nr_m[2] + 1, 2 * nr_m[2]);  kraus committed Apr 16, 2012 653 654 655  Index mirroredIE = 2*nr_m[0] - IE; Index mirroredJE = 2*nr_m[1] - JE;  kraus committed Apr 17, 2012 656  Index shiftedKE = KE - nr_m[2];  kraus committed Apr 16, 2012 657   658 659 660  rho2_m[I ][J ][KE] = ggrn2[I ][J ][shiftedKE]; rho2_m[IE][J ][aK] = rho2_m[mirroredIE][J ][aK ]; rho2_m[aI][JE][aK] = rho2_m[aI ][mirroredJE][aK ];  kraus committed Apr 16, 2012 661   662  IpplTimings::stopTimer(IntGreensMirrorTimer2_m);  kraus committed Apr 16, 2012 663 664 }  gsell committed Mar 15, 2012 665 666 667 668 669 670 671 672 673 674 675 Inform &FFTPoissonSolver::print(Inform &os) const { os << "* ************* F F T P o i s s o n S o l v e r ************************************ " << endl; os << "* h " << hr_m << '\n'; os << "* ********************************************************************************** " << endl; return os; } /*************************************************************************** * $RCSfile: FFTPoissonSolver.cc,v$ $Author: adelmann$ * $Revision: 1.6$ $Date: 2001/08/16 09:36:08$ ***************************************************************************/